Universal Stability Properties for Multilayer Hele-Shaw Flows and Application to Instability Control

With the motivation of understanding the effect of various injection policies currently in practice for chemical enhanced oil recovery, we study linear stability of displacement processes in a Hele-Shaw cell involving injection of an arbitrary number of fluid phases in succession. This work mainly builds upon our earlier study of the three-layer case [P. Daripa, Phys. Fluids, 20 (2008), 112101]. Stability results obtained for an arbitrary number of displacing fluids in succession reduce to the Saffman–Taylor case when there is only one displacing fluid. The stability results have been applied here to design injection policies that are considerably less unstable than the pure Saffman– Taylor case. In particular, two sets of parameters have been obtained that improve stability. Implementation of such injection policies based on the application of the stability results is likely to improve oil recovery.